54 



Mr. F. Galton. 



[Jan. 21, 



selected at random. In this latter case the quartile value of the 

 system of mid-parents would be l/->/2 .p = 121 inch. Now, I find the 

 quartile of the series of the mid-parental system obtained from the 

 two columns in Table III, that are headed respectively " Heights of 

 the mid-parents " and " Total number of mid-parents," to be 1*19 

 inches,* which is an unexpectedly exact accordance. 



(3.) Median Stature. I obtain the values 68*2, 68'5, 68*4, from the 

 three series mentioned above, but the middle value, printed in italics, 

 is a smoothed value. This is one of the only two smoothed values in 

 the whole work, and has been justifiably corrected because the one 

 ordinate that happens to accord closely with the median is out of 

 harmony with all the rest of the curve. This fortuitous discrepancy 

 amounts to more than 0*15 inch. It does not affect the quartile value, 

 because neither the upper nor the lower quartile is touched, and, 

 therefore, the half -interquartile remains unchanged. It must be 

 recollected that the series in question refers to R.F.F. brothers, which 

 are a somewhat conditioned selection from the general R.F.F. popula- 

 tion, and could not be expected to afford as regular an ogive as that 

 made from observations of men selected from the population at 

 hazard. It is undoubtedly in this group that the least accuracy was 

 to have been expected. 



Mean Ratios of Regression in the Primary Degrees of Kinship. — (1.) 

 From the stature of mid-parents of the same height, to the mean of 

 the statures of all their children. I have already (he. cit.) published 

 the conclusions to which I arrived about this, but it is necessary to 

 enter here into detail. The data are contained in Table III, where 

 each line exhibits the distribution of stature among the children of all 

 the mid-parents in my list, who were of the stature that forms the 

 argument to that line. The median stature in each successive line 

 is the mean stature of all the children, and is given at the side in the 

 column headed " Medians." Their values are graphically represented 

 in fig. 5. It will be there seen that these value are disposed about 

 a straight line. If the median statures of the children had been the 

 same as those of their mid-parents this line would have accorded with 

 the line AB, which, from the construction of the table, is inclined at 

 an angle of 45° to the line "Mean Stature of Population," which 

 represents the level of mediocrity. However, it does not do this, but 

 its position is inclined at a smaller angle, 0, such that 



tan 6 : tan 45 : : 2 : 3. 



This gives us the ratio of regression (=w) in the present case ; and, 

 therefore, in the notation I adopt w=§ . 



(2.) From the stature of men of the same height, to the mean of 

 the statures of all their children. "We have just seen that when both 



* In all my measurements the second decimal is only approximately correct. 



